Question

5. Fie a, b e R pentru care b - a = 3, b > 3. Arătaţi că valoarea expresiei
E(a, b) este-272, unde E(a, b) = radical a ^2 + b2 – 6b+ 9 - radical a^2+b+ 2(2a - b)+5.​

Answer 1

a, b∈R ; b - a = 3, b > 3   => a>0

=> a=b-3; b=a+3

E(a, b) = √(a²+ b²–6b+ 9) - √[a²+b²+ 2(2a - b)+5]

E(a,b)= √[a²+ (b-3)²]- √(a²+b²+ 4a -2b+4+1)

E(a,b)= √(a²+a²)-√[(a+2)²+(b-1)²]

E[a,b]= √(2a²)-√(a+2)²+(a+3-1)²]

E[a,b]= √(2a²)-√(a+2)²+(a+2)²]

E[a,b]= √(2a²)-√[2(a+2)²]

E(a,b)=a√2 - (a+2)√2

E(a,b)= √2(a-a-2)

E(a,b)= -2√2